Here is a video of a NYC taxi driver going up on 1st Ave catching green lights at every intersection from 1st to 125th St.* The driver spends a significant amount of time in a lane marked "BUS ONLY" which it seems buses sometimes use (e.g. see early in the 9th and 10th minutes), though they sometimes use the other side (e.g. third quarter of 2nd minute).
NYC's page on these lanes states "If you drive, park, or stand in a bus lane during hours of operation you face fines ranging from $115 to $150" (plus possible points against a license) and describes even automatic video enforcement, but the cab driver seems quite comfortable driving there. This video was taken on a Sunday night, so maybe the cab driver knew of an exception, which the rule statement seems to allow for (via language restricting the offense definition to "during hours of operation.")
How does one find out what hours those restrictions are in effect?
Even the Bus Rapid Transit page for the First Ave route does not seem to have an answer.
(*): Audio NSFW, and there is an odd jump in the video at 11:38.